Solve 3 * (y - 5) ^ 2 + 5y = (2y - 3) ^ 2 - (y + 1) ^ 2 + 1 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$3(y-5)^{2}+5y=(2y-3)^{2}-(y+1)^{2}+1$$

Solve for y

$y=6$

Steps for Solving Linear Equation

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(y-5\right)^{2}$.

$$3\left(y^{2}-10y+25\right)+5y=\left(2y-3\right)^{2}-\left(y+1\right)^{2}+1$$

Use the distributive property to multiply $3$ by $y^{2}-10y+25$.

$$3y^{2}-30y+75+5y=\left(2y-3\right)^{2}-\left(y+1\right)^{2}+1$$

Combine $-30y$ and $5y$ to get $-25y$.

$$3y^{2}-25y+75=\left(2y-3\right)^{2}-\left(y+1\right)^{2}+1$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2y-3\right)^{2}$.

$$3y^{2}-25y+75=4y^{2}-12y+9-\left(y+1\right)^{2}+1$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(y+1\right)^{2}$.

$$3y^{2}-25y+75=4y^{2}-12y+9-\left(y^{2}+2y+1\right)+1$$

To find the opposite of $y^{2}+2y+1$, find the opposite of each term.

$$3y^{2}-25y+75=4y^{2}-12y+9-y^{2}-2y-1+1$$

Combine $4y^{2}$ and $-y^{2}$ to get $3y^{2}$.

$$3y^{2}-25y+75=3y^{2}-12y+9-2y-1+1$$

Combine $-12y$ and $-2y$ to get $-14y$.

$$3y^{2}-25y+75=3y^{2}-14y+9-1+1$$

Subtract $1$ from $9$ to get $8$.

$$3y^{2}-25y+75=3y^{2}-14y+8+1$$

Add $8$ and $1$ to get $9$.

$$3y^{2}-25y+75=3y^{2}-14y+9$$

Subtract $3y^{2}$ from both sides.

$$3y^{2}-25y+75-3y^{2}=-14y+9$$

Combine $3y^{2}$ and $-3y^{2}$ to get $0$.

$$-25y+75=-14y+9$$

Add $14y$ to both sides.

$$-25y+75+14y=9$$

Combine $-25y$ and $14y$ to get $-11y$.

$$-11y+75=9$$

Subtract $75$ from both sides.

$$-11y=9-75$$

Subtract $75$ from $9$ to get $-66$.

$$-11y=-66$$

Divide both sides by $-11$.

$$y=\frac{-66}{-11}$$

Divide $-66$ by $-11$ to get $6$.

$$y=6$$